1 / 27

Decoherence at optimal point: beyond the Bloch equations

Decoherence at optimal point: beyond the Bloch equations. Yuriy Makhlin. Landau Institute. A. Shnirman (Karlsruhe) R. Whitney (Geneva) G. Schön (Karlsruhe) Y. Gefen (Rekhovot) J. Schriefl (Karlsruhe / Lyon) S. Syzranov (Moscow)

anakin
Download Presentation

Decoherence at optimal point: beyond the Bloch equations

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Decoherence at optimal point:beyond the Bloch equations Yuriy Makhlin Landau Institute A. Shnirman (Karlsruhe) R. Whitney(Geneva) G. Schön (Karlsruhe) Y. Gefen (Rekhovot) J. Schriefl (Karlsruhe / Lyon) S. Syzranov (Moscow) Quantronics group: G. Ithier, E. Collin, P. Joyez, P. Meeson, D. Vion, D. Esteve (Saclay)

  2. Outline • Josephson qubits & decoherence sources • Bloch equations, applicability • Beyond Bloch equations: • 1/f noise • optimal points, higher-order terms: X2, X4 • FID and echo at optimal point - time-dependent field, Berry phase

  3. Coherent oscillations and decoherence noisy environment qubit Pashkin et al. `03 random phase, decoherence P=|s+ | • Analyze decay of coherence: • dephasing time • short-time asymptotics • (important for QEC) • decay law t qubits as spectrometers of quantum noise

  4. Power spectrum: , Models for noise and classification longitudinal – transverse – quadratic (longitudinal) … X – fluctuating field , e.g.: • Gaussian noise with given spectrum • collection of incoherent fluctuators • bosonic bath • spin bath non-gaussian effects – cf. Paladino et al. ´02 Galperin et al. ´03

  5. Longitudinal coupling  “pure” dephasing X – classical or quantum field for regular spectrum for 1/f noise e.g., Cottet et al. 01

  6. Transverse coupling  relaxation Golden Rule:

  7. S(w) 1/c 1/c c¿ T1, T2 works for 1/T1 1/T2* weak short-correlated noise w 0 DE/~ Bloch equations, applicability Bloch (46,57) Redfield (57) perturbation theory Dt Dt Dt at c¿ t ¿ T1, T2: weak and uncorrelated on neighboring  t‘s t

  8. Beyond Bloch equations • 1/f noise – long correlation time c • optimal operation points: X2 or higher powers • sharp pulses (state preparation) • time-dependent field, Berry phase Study: decay of coherence P(t)=h+(t)i

  9. -1 Fx/F0 0.5 1 Vg Quantronium Charge-phase qubit Vion et al. (Saclay) E1 operation at saddle point E0

  10. p/2 p/2 Decay of Ramsey fringes at optimal point Vion et al., Science 02, …

  11. 2 1 H= - (DE+lX )s p/2 p/2 2 z p/2 p/2 p Longitudinal quadratic coupling, non-Gaussian effects Free induction decay (Ramsey) Echo signal

  12. Line shape: Determinant regularization Linked cluster expansion for X21/f

  13. similar: Rabenstein et al. 04 Paladino et al. 04 in general even more general 1/f spectrum „quasistatic“ for linear coupling For optimal decoupled pointX2 X4:

  14. Fitting the experiment G. Ithier et al. (Saclay)

  15. High frequency contribution w f

  16. Gaussian approximation and accurate calculation

  17. adiabaticity + transverse X -> longitudinal X^2 YM, Shnirman `03 X(t) B0 DE ¼ B0 + X2/2B0 DE useful: - consider transverse and longitudinal noise together - treat several independent noise sources - explains „non-Gaussian“ effects of bistable fluctuators (reduces to Gaussian in X^2; cf. Paladino et al. `02)

  18. Example: TLF‘s and the qubit transverse coupling to TLF‘s (Paladino et al. ‘02): (t) = 0,v ) (2(t)/2 ) = 0, v´ v´= v2/2 (t) P(t) = e-t/(2T1)¢ P‘(t)  for symmetric coupling = v/2, -v/2 - no dephasing for one strong TLF (vÀ) or many weak TLFs: it is enough to use the Golden rule =h X2i/2 1/T2=v‘2/(4)

  19. Echo for 2 1/t 1/t 1 e-f t /2

  20. Quasi-static environment

  21. N=4 periods between -pulses p/2 p p p p/2 Multi-pulse echo for quadratic 1/f noise cf.: NMR; Viola, Lloyd `98; Uchiyama, Aihara `02 contributions of frequency ranges: f t<<1 1¿ft¿ N N¿ft

  22. N=4 p/2 N=30 N=20 N=10 FID analyt P(t) =10-6 =104 p p p p/2 Multi-pulse echo for quadratic 1/f noise cf.: NMR; Viola, Lloyd `98; Uchiyama, Aihara `02 all perturbative orders involved smooth decay with N

  23. Many noise sources in general, E(V,) has extrema w.r.t. parameters (V,) 2e- and 0-periodic => torus => 1min, 1max, 2 saddles E=  V2 + 2 +  V  - cross-term But: no cross-term for H = H(V) + H() still, cross-terms for flux qubits

  24. Many noise sources two uncorrelated comparable noise sources: reduces to the problem for one source: (for similar noise spectra of X and Y) Remark: subtleties for 1/f noises w/ different infrared cutoffs

  25. Decoherence close to optimal point or

  26. Berry phase in dissipative environment Whitney, YM, Shnirman, Gefen ‘04 Geometric complex correction BP - monopole correction - quadrupole

  27. Summary • decoherence beyond the Bloch equations • effects of Gaussian 1/f noise: • - describes large number of weak fluctuators • - non-Gaussian effects for (effective) quadratic coupling • - single- and multi-pulse echo experiments • - non-trivial decay laws • - benchmark! • decoherence in the vicinty of optimal point • effect of several noise sources • geometric phase and noise

More Related